# Full text of "Mathematical And Physical Papers - Iii"

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```ON  THE  MOTION OF  PENDULUMS.
109
T		n
calc.             obs.             diff.
( 3	1-549	1-27	-•279
Another sphere of wood Diameter 6f inches Weight in water 2102 grains	4 \  6 1  9 12	1-557 1-570 1-585 1-599	1-394 1-487 1-566 1-569	-•163 -•083 -•019 -•030
Vl8	1-621	1-565	-•056
Same   sphere   weighing   in ) water 3204 grains               j	10-85	1-594	1-634	+ •040
( 3	1-549	1-651	4- '102
1 4 Same sphere weighing in water J ^		1-557 1-570	1-627 1-654	+ •070 + •084
4204 grains	9	1-585	1-664	+ •079
\12	1-599	1-674	+ •075
70. If we strike out the experiments with the large sphere, which cannot well be compared with theory for a reason which will be explained further on, it will be observed that in seven out of the eight groups of experiments left, the signs in the last column are regularly minus. The preponderance of negative errors could be destroyed by using a much smaller value of y'//,' in the reduction. We have seen, however, that the value of vX deduced from Coulomb's experiments on the decrement of the arc of oscillation of disks satisfied almost exactly Bessel's observations of the time of oscillation of a sphere about two inches in diameter oscillating in water. The very small errors which remained in this case had both the sign +, whereas in Dubuat's experiments on the 1-inch and 2-J- inch spheres, the errors, which are far larger, have all the sign —. Since the experiments of Dubuat and Bessel, though made under similar circumstances, do not lead to the same result, it is of course impossible for any theory to satisfy them both. The numbers in the last column of the preceding table are, however, far too regular to be attributable to mere fortuitous errors of observation. If we suppose Bessel's results to have been nearly exact, there must have been something in the mode either of making or of reducing Dubuat's experiments which caused a tendency to error in one direction.
With respect to the reduction of the experiments it may be observed that the length I was measured from the centre of```